Question

• Consider the function 2f(t)=1−2t+4t2. What is the relative rate of change when 2t=2? Give your answer to one decimal place.

To find the relative rate of change, calculate f′(2), which is the derivative of f(t) evaluated at t=2.

Answer 1

To find the relative rate of change, divide the function by 2, take the derivative using the power rule, and evaluate it at t = 2. The relative rate of change is 14.

Step-by-step explanation:

To find the relative rate of change, we need to calculate the derivative of the function. First, let's divide the function by 2 to get f(t) alone: f(t) = (1 - 2t + 4t^2) / 2. Take the derivative of f(t) using the power rule, which states that d/dx(x^n) = n*x^(n-1), and evaluate it at t = 2.

The derivative of f(t) is f'(t) = -2 + 8t. Evaluating it at t = 2, we get f'(2) = -2 + 8(2) = -2 + 16 = 14.

Therefore, the relative rate of change when 2t = 2 is 14.